The lifetime in months of a transistor in a certain application is random with probability density function: f(x) = {0.4e^-0.4x, x>0 0, x<0

a. Compute the mean lifetime.

b. Compute the standard deviation of the lifetimes.

c. Compute the cumulative distribution function of the lifetime.

d. Compute the probability that the lifetime will be less than 6 months.

e. Compute the 60^th percentile of the lifetime.

Explained below.

Step-by-step explanation:

The probability density function of lifetime in months of a transistor in a certain application is:

The probability density function suggests that the random variable X follows a exponential function with parameter λ = 0.4.

(a)

Compute the mean lifetime as follows:

Thus, the mean lifetime is 2.5 months.

(b)

Compute the standard deviation of the lifetimes as follows:

Thus, the standard deviation of the lifetimes is 2.5 months.

(c)

The cumulative distribution function of the lifetime is:

(d)

Compute the probability that the lifetime will be less than 6 months as follows:

Thus, the probability that the lifetime will be less than 6 months is 0.9093.

(e)

Compute the 60th percentile of the lifetime as follows:

Thus, the 60th percentile of the lifetime is 2.3 months.

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

6/20

step-by-step explanation: